Equidistribution towards the Green current

Vincent Guedj

Bulletin de la Société Mathématique de France (2003)

  • Volume: 131, Issue: 3, page 359-372
  • ISSN: 0037-9484

Abstract

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Let f : ℙ k → ℙ k be a dominating rational mapping of first algebraic degree λ ≥ 2 . If S is a positive closed current of bidegree ( 1 , 1 ) on ℙ k with zero Lelong numbers, we show – under a natural dynamical assumption – that the pullbacks λ - n ( f n ) * S converge to the Green current T f . For some families of mappings, we get finer convergence results which allow us to characterize all f * -invariant currents.

How to cite

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Guedj, Vincent. "Equidistribution towards the Green current." Bulletin de la Société Mathématique de France 131.3 (2003): 359-372. <http://eudml.org/doc/272445>.

@article{Guedj2003,
abstract = {Let $f:\mathbb \{P\}^k \rightarrow \mathbb \{P\}^k$ be a dominating rational mapping of first algebraic degree $\lambda \ge 2$. If $S$ is a positive closed current of bidegree $(1,1)$ on $\mathbb \{P\}^k$ with zero Lelong numbers, we show – under a natural dynamical assumption – that the pullbacks $\lambda ^\{-n\}(f^n)^*S$ converge to the Green current $T_\{\hspace\{-0.55542pt\}f\}$. For some families of mappings, we get finer convergence results which allow us to characterize all $f^*$-invariant currents.},
author = {Guedj, Vincent},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Green current; holomorphic dynamics; volume estimates},
language = {eng},
number = {3},
pages = {359-372},
publisher = {Société mathématique de France},
title = {Equidistribution towards the Green current},
url = {http://eudml.org/doc/272445},
volume = {131},
year = {2003},
}

TY - JOUR
AU - Guedj, Vincent
TI - Equidistribution towards the Green current
JO - Bulletin de la Société Mathématique de France
PY - 2003
PB - Société mathématique de France
VL - 131
IS - 3
SP - 359
EP - 372
AB - Let $f:\mathbb {P}^k \rightarrow \mathbb {P}^k$ be a dominating rational mapping of first algebraic degree $\lambda \ge 2$. If $S$ is a positive closed current of bidegree $(1,1)$ on $\mathbb {P}^k$ with zero Lelong numbers, we show – under a natural dynamical assumption – that the pullbacks $\lambda ^{-n}(f^n)^*S$ converge to the Green current $T_{\hspace{-0.55542pt}f}$. For some families of mappings, we get finer convergence results which allow us to characterize all $f^*$-invariant currents.
LA - eng
KW - Green current; holomorphic dynamics; volume estimates
UR - http://eudml.org/doc/272445
ER -

References

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